[Mristudio-users] difference between ADC and MD

[Venkatesh Rajagopalan]

Thanks very much Hangyi,

Venkat

From: mristudio-users-bounces at mristudio.org [mailto:mristudio-users-bounces at mristudio.org] On Behalf Of Hangyi Jiang
Sent: Thursday, February 14, 2013 2:12 PM
To: DTI Studio, ROI Editor, DiffeoMap Questions/Support
Subject: Re: [Mristudio-users] difference between ADC and MD

hi,

apparent diffusion coefficient (ADC) is a measurement for a diffusion weighted image in a specific gradient. its definition is:

ADC = ln(S/S0) / (-b)
here, S is the gradient weighted image, S0 is the B0 image, b is the b value.

so, if a data set has 30 gradient orientations, there will be 30 ADCs.  for each gradient, there will be a ADC map for this particular DW-image.


mean- diffusivity is defined as the mean value of eigen values (Lamda 1-3) of the tensor ellipsoid:
Mean_Diffusivity = (Lamda_1 + Lamda_2 + Lamda_3) / 3;

mathematically, this is equal to the average of the diagonal elements of the tensor matrix:
Mean_Diffusivity =  (Dxx + Dyy + Dzz) / 3;

in noise-free situation (practically, it is impossible), mean-diffusivity is also equal to the mean value of ADCs of the DWI data set.
e.g. given a data set with 30 orientations, then Mean_Diffusivity = (ADC1 + ADC2 + .. ADC30) / 30;

BTW: the sum of eigen-values or the sum of the diagonal elements of the tensor matrix is called TRACE:
TRACE =  (Lamda_1 + Lamda_2 + Lamda_3) = (Dxx + Dyy + Dzz);

so, Mean_Diffusivity = TRACE/3;


best,

hangyi



________________________________
From: mristudio-users-bounces at mristudio.org<mailto:mristudio-users-bounces at mristudio.org> [mristudio-users-bounces at mristudio.org] on behalf of Venkatesh Rajagopalan [VRajagopalan at kesslerfoundation.org]
Sent: Thursday, February 14, 2013 1:40 PM
To: 'DTI Studio, ROI Editor, DiffeoMap Questions/Support'
Subject: [Mristudio-users] difference between ADC and MD
Hi All,

I very often come across apparent diffusion coefficient and mean diffusivity being measured in studies. I am wondering what is the difference between these two measures in terms of the formula used.

Thanks
Venkat

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